The sides of an isosceles triangle are 596 and the base is 408. Find the radius of the inscribed circle.

Given:

triangle – isosceles;

a = 596 (the length of the side of the triangle);

b = 408 (base of triangle).

Find:

radius of the inscribed circle (r).

The radius of a circle inscribed in an isosceles triangle is determined by the formula:

r = (b / 2) * (√ (2a – b) / (2a + b)).

We calculate the radius of a circle inscribed in a given isosceles triangle:

r = (408/2) * (√ (2 * 596 – 408) / (2 * 596 + 408));

r = 204 * (√ (1192 – 408) / (1192 + 408));

r = 204 * √ (784/1600);

r = 204 * √0.49;

r = 204 * 0.7;

r = 142.8.

Answer: 142.8.